We consider a linear model with heteroskedasticity of
unknown form. Using Stone's (1977, Annals of Statistics
5, 595–645) k nearest neighbors (k-NN)
estimation approach, the optimal weightings for efficient
least absolute deviation regression are estimated consistently
using residuals from preliminary estimation. The reweighted
least absolute deviation or median regression estimator
with the estimated weights is shown to be equivalent to
the estimator using the true but unknown weights under
mild conditions. Asymptotic normality of the estimators
is also established. In the finite sample case, the proposed
estimators are found to outperform the generalized least
squares method of Robinson (1987, Econometrica
55, 875–891) and the one-step estimator of Newey
and Powell (1990, Econometric Theory 6, 295–317)
based on a Monte Carlo simulation experiment.